Sentence Structure & Punctuation

Sometimes while writing a story, I like using short sentences. But I think I may be breaking a dozen punctuation rules while doing that! For example, this text.

I figured I had had enough. I narrowed my eyes, briskly. There was a skill to it you know; narrowing ones eyes.
I whispered amongst the stars, “Oye where did you run off to?” My ears perked. My limbs jumpy. My insides tangled. Ready to attack. Or run. Whatever the situation called for. A faint harrowing noise came by. I heard it. Gushing like the wind. Laughing like the stream. Cluck-cluck, I clucked my tongue. I SHALL NOT BE LAUGHED AT. I firmly shook my head, and I pounced. It took centuries for me to cross the bridge. Decades to land on the other side. But I was finally there. And I saw him. His nose a-quivering. His tail a-shivering. A grin on my face, I lunged.
*Gulp*
That was the end of his story. I licked my paws clean. Never get blood on your hand, they say. Those wise creatures. The stars.

I am doing this completely wrong? Should I use commas, etc and start joining my tiny sentences?
Also, this is my first post here, so please forgive me if this type of question has already been covered or something.

I think there are times and places for short sentences and sentence fragments. They can be very effective when used as parts of a symphony of sentences of all kinds. But a barrage of nothing but choppiness is something I find hard - very hard - to read.

As they said, there is a time and a place for short sentences and sentence fragments. For example, say you are writing a fast paced scene with a lot of excitement. You would not want long eloquent sentence chains when you want to convey how a character is rushed and his or her attention is changing every second. Likewise, if you are describing a dinner scene, you wouldn't necessarily want to use short, broken observations in plance of a calm fluid projection of the scene. You may intermix them for stylistic effect as such if you so choose:

I went down to dinner. Mother had called me five minutes ago, but I could not bring mysef to face my family with this secret looming over me. The excitement at the table was a dead give-away to my thought as I sat there quietly. I was the only one who didn't speak. They looked at me one by one. I felt their stares and my heart raced....